Were there any direct or immediate financial/banking policies made because of this recession? I've read that a combination of factors helped get America out of the Panic, but it never mentioned a reform in those policies.
The Panic of 1837 proved that the "cure was worse than the disease." Thus, it set the U.S. on the road to the passage of the 16th Amendment, and the establishment of the Federal Reserve some 76 years later, in 1913.
The "disease" that Jackson fought was a centralized national bank along the lines of the Bank of England, advocated by banker Nicholas Biddle.
The Jacksonian "cure" for America's banking woes was a number of small, decentralized, and undercapitalized banks, many of which collapsed in the Panic of 1837, leading to a depression. This experience convinced many Americans that they needed a central, or at least a very large, bank.
Around the turn of the 19th and 20th centuries J.P.Morgan created a large bank that bore his name (until the merger with Chase) that the Europeans considered the "unofficial" central bank of the United States. But the Crash of 1907 convinced the country that it needed an even stronger central bank, leading to the 16th Amendment to the Constitution providing for a central currency, the Federal Reserve, and the income tax.